You may also like

A Close Match

Can you massage the parameters of these curves to make them match as closely as possible?

Prime Counter

A short challenge concerning prime numbers.

The Right Volume

Can you rotate a curve to make a volume of 1?

Happy birthDay

Age 16 to 18
Challenge Level

This solution is not 'complete', but does indicate why the formula works. It will make more sense if you test it out using a spreadsheet.

This tasks seems daunting at first but then you might realise that essentially the function is a 'counter' and the year starts at 1st March and ends on 28/9th of February.
 
Years are always of the same structure with the exception of the last day of Feb:
 
From  1st March to 1st April is +31 days. 
 
From 1st April to 1st May is +30 days.
 
From 1st May to 1st June is +31 days.
 
etc.
 
For weekday calculations we are only interested in mod 7 changes. Since 31 is 3 mod 7 and 30 is 2 mod 7 we have the following differences between the first of the months, with the +0/1 corresponding to February.
 
(1Mar) +3, +2, +3, +2, +3, +3, +2, +3, +2, +3, +3,+0/1 (1Mar)

 Accumulating the changes from the 1st March (mod 7) gives
 
(1Mar) 0
(1Apr) 3
(1May) 5
(1Jun) 1
(1Jul) 3
(1Aug) 6
(1Sep) 2
(1Oct) 4
(1Nov) 0
(1Dec) 2
(1Jan) 5
(1Feb) 1
(1Mar) 1 or 2 in a leap year
 
Interestingly, the $\mbox{int}\left[\frac{(m+1)\times 26}{10}\right]$ part matches these offsets with the labellings of months given  (try it out to see).
 
 
So, in the absence of leap years the expression would work.
 
The part $y+\mbox{int}\left[\frac{y}{4}\right]+\mbox{int}\left[\frac{C}{4}\right]-2C$ has the correct mod 7 behaviour to count the leap years (try it).